Experiments In Mathematics Using Maple

The book is designed for use in school computer labs or with home computers running the computer algebra system Maple.

The book is designed for use in school computer labs or with home computers running the computer algebra system Maple.

As discrete mathematics rapidly becomes a required element of undergraduate mathematics programs, algebraic software systems replace compiled languages and are now most often the computational tool of choice. Newcomers to university level mathematics, therefore, must not only grasp the fundamentals of discrete mathematics, they must also learn to use an algebraic manipulator and develop skills in abstract reasoning. Experimental Mathematics with MAPLE uniquely responds to these needs. Following an emerging trend in research, it places abstraction and axiomatization at the end of a learning process that begins with computer experimentation. It introduces the foundations of discrete mathematics and, assuming no previous knowledge of computing, gradually develops basic computational skills using the latest version of the powerful MAPLE® software. The author's approach is to expose readers to a large number of concrete computational examples and encourage them to isolate the general from the particular, to synthesize computational results, formulate conjectures, and attempt rigorous proofs. Using this approach, Experimental Mathematics with MAPLE enables readers to build a foundation in discrete mathematics, gain valuable experience with algebraic computing, and develop a familiarity with basic abstract concepts, notation, and jargon. Its engaging style, numerous exercises and examples, and Internet posting of selected solutions and MAPLE worksheets make this text ideal for use both in the classroom and for self-study.

This text introduces students to an experimental approach to mathematics, using Maple to systematically investigate and develop mathematical theory.

With the continued advance of computing power and accessibility, the view that "real mathematicians don't compute" no longer has any traction for a newer generation of mathematicians. The goal in this book is to present a coherent variety of accessible examples of modern mathematics where intelligent computing plays a significant role and in so doi

Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple applications, the reader is given tools for creating the shapes that are being studied. Thus, you can "see" a fluid rising up an inclined plane, create minimal surfaces from complex variables data, and investigate the "true" shape of a balloon. Oprea also includes descriptions of experiments and photographs that let you see real soap films on wire frames. The theory of minimal surfaces is a beautiful subject, which naturally introduces the reader to fascinating, yet accessible, topics in mathematics. Oprea's presentation is rich with examples, explanations, and applications. It would make an excellent text for a senior seminar or for independent study by upper-division mathematics or science majors.

This unusual introduction to Maple shows readers how Maple or any other computer algebra system fits naturally into a mathematically oriented work environment. Designed for mathematicians, engineers, econometricians, and other scientists, this book shows how computer algebra can enhance their theoretical work. A CD-ROM contains all the Maple worksheets presented in the book.

This book is based on the research papers presented during The Institute of Industrial Engineers Asian Conference 2013 held at Taipei in July 2013. It presents information on the most recent and relevant research, theories and practices in industrial and systems engineering. Key topics include: Engineering and Technology Management Engineering Economy and Cost Analysis Engineering Education and Training Facilities Planning and Management Global Manufacturing and Management Human Factors Industrial & Systems Engineering Education Information Processing and Engineering Intelligent Systems Manufacturing Systems Operations Research Production Planning and Control Project Management Quality Control and Management Reliability and Maintenance Engineering Safety, Security and Risk Management Supply Chain Management Systems Modeling and Simulation Large scale complex systems